Answer:
○ [tex]3x + 4y = 7[/tex]
Step-by-step explanation:
The general form of the equation of a straight line is as follows:
[tex]\boxed{y = mx + c}[/tex],
where:
m = slope
c = y-intercept.
This means that m, which is the coefficient of [tex]x[/tex], needs to be [tex]-\frac{3}{4}[/tex].
Therefore we have to rearrange each equation given to make y the subject, and then check if the coefficient of [tex]x[/tex] becomes [tex]-\frac{3}{4}[/tex].
• First option:
[tex]4x - 3y = 7[/tex]
⇒ [tex]-3y = -4x + 7[/tex]
⇒ [tex]y = \frac{4}{3}x -{ \frac{7}{3}[/tex]
∴ 'm' is [tex]\bf \frac{4}{3}[/tex], not [tex]-\frac{3}{4}[/tex], therefore this option is incorrect.
• Second option:
[tex]4x + 3y = 7[/tex]
⇒ [tex]3y = -4x + 7[/tex]
⇒ [tex]y = -\frac{4}{3}x + \frac{7}{3}[/tex]
∴ 'm' is [tex]\bf -\frac{4}{3}[/tex], not [tex]-\frac{3}{4}[/tex], therefore this option is incorrect.
• Third option:
[tex]3x + 4y = 7[/tex]
⇒ [tex]4y = -3x + 7[/tex]
⇒ [tex]y = -\frac{3}{4}x + \frac{7}{3}[/tex]
'm' is [tex]\bf -\frac{3}{4}[/tex], therefore this option is correct.
Note:
You can rearrange the equation given in the last option, and see that 'm' comes out to be [tex]\frac{3}{4}[/tex], thereby making it incorrect.
